A difficulty to answer is that there is only an image joint to the question. Data of the points lying on the border between the black area and the white area is difficult to obtain from scanning.

Your "fitted ellipse" (red curve on your joint image) seems with vetical axis. This supposes that your model equation if of this kind (Four parameters only) :

In fact the elipse appears slightly inclined. Thus the fitting is better in using the general equation of elliptic curve ( Five parameters ) :

Small deviation remain at low values of y, close to the staight part not drawn on the figure. The cause is probably that the "elliptic" part is not realy elliptic. May be it is a segment of inclined "fish curve" or even more general a quartic curve (14 parameters).

https://mathworld.wolfram.com/FishCurve.html

https://mathworld.wolfram.com/QuarticCurve.html